A Shelton High School teacher being investigated by the police department for possible “inappropriate conduct” with students resigned Wednesday.

The Valley Independent Sentinel has the teacher’s name but decided not to publish it Wednesday since no criminal charges were filed and the teacher in question could not be reached for comment.

School Superintendent Freeman Burr said Shelton High School headmaster Beth Smith received information Friday about the teacher. She told Burr. Smith contacted the police department and the state Department of Children and Families, Burr said.

“We met and we felt that there was some credibility to what was being reported,” Burr said. “On Friday, Dr. Smith contacted the appropriate authorities.”

Burr would not comment on any details of the allegations made against the teacher.

The teacher was put on administrative leave Monday.

Shelton police confirmed the investigation Wednesday afternoon through a press release. It is posted at the end of this story. No arrests have been made, police said.

Parents and students at the school told the Valley Independent Sentinel that the incident involves a teacher who had inappropriate communication with a student. There were conflicting reports of whether the contact was through e-mail or cell phone messages.

Police wouldn’t confirm those details — but said more than one student is involved.

Police gave few details about what conduct may have occurred, saying they were still gathering information.

Detective Ben Trabka said police are working with the school district and DCF to investigate.